DE2155470B2 - Method for digitally determining the position of the zero crossings of a sinusoidal alternating current signal - Google Patents

Description

The invention relates to a method for digitally determining the position of the zero crossings a sinusoidal alternating current signal.

In the German Auslegeschrift 1 176254 is one Circuit arrangement for monitoring maximum and minimum values of the alternating current magnitude one of this circuit arrangement galvanically separated control circuit described, in addition to others Components contains a pulse shaper stage that responds to the zero crossings of the alternating current quantity.

Various malfunctions or errors occur in electrical power networks, of which in particular short circuits between power lines or between power lines and earth as a result of lightning strikes are important examples. Against such disturbances power grids require effective protection. Protection relays are currently used for this purpose It is common to have different protective relay systems depending on the type of power network to be protected be summarized.

Protection relays are mostly used, for example, to detect a fault Undervoltage as well as the distance or the direction of the disturbance are suitable, through corresponding analog Realized circuits that are set up for the corresponding function. In practice, therefore, turn out to be For the effective protection of a high-voltage network, protective relays of this type in large numbers than necessary. This is disadvantageous in that such protective relays not only cause high manufacturing costs, but also can also cause considerable difficulties in their monitoring and maintenance.

Based on the more recent development of digital computers, attempts have therefore already been made to develop the known Replace protective relays with universal digital computers. Given by a protection relay The required high operational reliability are, of course, also required of one to provide digital computers used as a replacement for protective relays, through appropriate experiments was made by G. D. Rock fei! Er in a work entitled "Fault Protection with a Digital Computer" (Paper No. 68 TP 625-PWR) at the IEEE Summer Power Meeting, July 23-28, 1968, and by G. D. Rock fei ler and E.A. Udren in a job with the title "High-speed Distance Relaying Using a Digital Computer" (Paper No. 71 TP567-PWR) at the IEEE Summer Meeting and International Symposium on High Power Testing, from 18. to July 23, 1970, reported.

Both works clearly show that there is a strong need to replace the known protective relay consists of digital computers.

The invention is therefore based on the object of specifying a way in which the parameters of alternating current signals, such as those of importance for the functional sequence in protective relays are, and in particular the timing of the zero crossings of the alternating current signals in purely digital Let determine wise.

This object is achieved according to the invention in that the alternating current signal is sampled in its amplitude A (t) with a fixed sampling period Ii = t "- (" _ !, which is less than half the period T of the alternating current signal, so that the determined amplitude values are stored over a predeterminable time and are multiplied in pairs for two consecutive scans so that the sign of the amplitude value products obtained is determined and that

for each amplitude value pair / l (t _n _i) and A (I _n ), for which a product A (^ ₁ ) -A (t _n ) s? 0 results, the point of intersection of the abscissa is calculated for a straight line passing through these amplitude values.

With the aid of the amplitude values determined directly within the scope of the invention on the one hand and the on On the other hand, zeros of the treated alternating current signals calculated using these amplitude values practically all relevant determinants for the alternating current signals can be determined derive, where as examples the frequency and the maximum values of an alternating current signal, the phase difference between two different AC signals and the AC impedance and the AC power for a consumer can be named.

The method according to the invention thus enables a purely digital recording of all items to be determined An AC signal and, for example, the simulation of the analog functions of Protection relays, as they have been customary for the protection of high-voltage networks up to now.

For the following further explanation of the invention, reference is made to the drawing; thereby shows in the drawing

1 shows a signal diagram to explain the basic principle of the invention,

F i g. 2 shows a signal diagram to explain how the invention is used in particular for detecting the frequencies is used by sinusoidal signals,

F i g. 3 shows a signal diagram to explain how the invention is used, in particular, to detect a phase difference is used between sinusoidal signals,

4a to 4k are signal diagrams for explaining the possible discrimination or differentiation of waveforms that occur between, sinusoidal signals in the case of phase difference detection as in FIG. 3 appear,

F i g. 5 shows the basic block diagram of an embodiment according to the invention,

F i g. 6 an impedance diagram to explain the conductance characteristic of a protective relay,

7 shows a program flow chart for the detection of the zeros of alternating current signals,

8 shows a program flow chart for the detection of phase differences between sinusoidal alternating current signals,

F i g. 9 is a program flow chart showing the function of a frequency relay;

10 is a program flow chart showing the function of a peak value detection relay;

11 is a program flow chart showing the function of a power measurement relay,

Fig. 12 is a program flow chart showing the function of an impedance relay, and

13 shows the structure of the discriminator or decision-maker stage in the block diagram in Fig. 5, with units each performing a single function and the program flow chart in FIG. 8 realize.

F i g. 1 shows, in a Cartesian coordinate system, a sinusoidal alternating current signal A (t), hereinafter referred to as alternating current signal for short, the amplitude of which varies with time, the abscissa and the ordinate indicating the time and the amplitude, respectively. F i g. 1 indicates how the zeros of the alternating current signal A (ή are detected according to the method according to the invention.

It is initially assumed that the amplitude of the alternating current signal A (t) at one point in time is I ₁ / 4U ₁ ), while at another point in time t _{2 it has} the value A (I ₂ ) , as can be readily seen from FIG is. When the following inequality holds:

A (I ₁ ) -A (I ₂ ) ^ O, (1)

A zero point of the alternating current signal ^ U) must lie between the two times t _x and t ₂ , that is, A (t) becomes equal to zero for a time t which satisfies the equation: t _t ^ i ^ r ₂ . This is always correct when the interval A t between I ₁ and t _{2 is} shorter than the period T of the alternating current signal A (t) .

Assuming that the zero point of the alternating current signal Λ (t) lies between r ₁ and t 2, consider the relationship between, on the one hand, a point in time t _u (which should be zero) on the abscissa, where a straight line through the point A (I ₁ ) , and the point representing A (t ₂ ) intersects the abscissa and, on the other hand, a point in time t ₁₂ (actually zero) on the abscissa where A U) becomes zero, that is,, 4 (J ₁₂ ) = 0. It is known that if the scores! and t _{2 are} suitably chosen, the points t _n and i _{12 can} coincide. With any choice of I ₁ and t ₂ , however, they usually differ from one another. The time interval A t _n from T ₁ to I ₁₁ and the time interval Δ t _l2 from t _n to I ₂ are given by the following expressions:

^Ahl ~

At "=

Uu ₂ ) I

At, (2)

At. (3)

Referring to FIG. 1, it follows that hi = h + Δ t _n . Therefore, the assumed zero A U ₁ ,) of the AC signal XU) can be obtained. Let us now examine the difference between the points t _u and t ₁₂ , ie the deviation Δ t _a in the event that the abscissa t ₁₂ , which gives the actual zero value A (t ₁₂ ) , is obtained approximately by using the abscissa I ₁₁ which gives the assumed zero value A (t _n ) , and expressions (2) and (3) above. It follows from approximate or recursive calculations, if many arbitrary values that are smaller than half of the period 7 of the alternating current A (t) are substituted for At , that the deviation A t _{a is} at most equal to about V ₃₆ sr radians (= 5 ° ) in terms of the phase angle! which are assigned to the alternating current signal A (t) when / 1 1 takes values smaller than T / 4 .

Accordingly, the invention relates to a method for calculating the zero point of the alternating current signal A (t) using the above expressions (1). (2) and (3), using a sampling signal which has a sampling period .1 1 that is shorter than a quarter of the period T of the AC signal A (t) . The invention also provides a method for digitally processing alternating current on the basis of such zeros as obtained in the manner previously explained, which method can achieve the same result as with a protective relay system currently in use.

F i g. FIG. 2 is a signal diagram for explaining the extraction of the zero deviation, as has been described in connection with FIG. 1, especially for the frequency detection of the alternating current signal A (t). The alternating current signal A (i) is sampled at times r ₁ , t 2, f ₃ ... t ₁₄ ..., the

Sampling period, Ir is chosen so that ..Ir <χΓ.

when T is the period of the AC signal A (t) . As can be seen from the previous explanation with reference to FIG. 1, the products / Kr ₁ ) * A (t ₂ ), AU ₁ ) * / IU ₈ ) and A (t _l3 ) * A (t _l4 ) are all negative: where / IUi), ^ U ₇ ) and -4 (t ₁₃ ) are the instantaneous values of the alternating current signal A (r), which _{is sampled at times r ,, r 7} and r, ₃ , and further A (I ₂ ), / IU ₈ ) and A (t _1A ) the instantaneous values of A (t), sampled at times r ₂ , r ₈ and r ₁₄ , which after a sampling period I f follow _{the times r 1 , r 7} and f 13, respectively. It can also be seen that at r ₂ , r ₈ and I ₁₄ zeros occur between r ₁ and r 2, r ₇ and r ₈ and r _I3 and t ₁₄ . As a result, the times, U ₁₁ , If ₁₂ , .It ₁ ',, IrJ ₂ , .U ₁ "or At {' _{2 can range} from r, to the first zero, from r ₂ to the first zero, from r ₇ to to the second zero, from r ₈ to the second zero or from r ₁₃ to the third zero and from f ₁₄ to the third zero (see FIG. 1) using the method explained in FIG

Period T and its half-period -y are then given by the following equations:

- = 5 Ir + Ir ₁₂ + W ₁ ',,

T = ll.fi + 1 f _{] 2} + Ir ₁ ','

(4)

(5)

35

Accordingly, by calculating the reciprocal of T from the above formula 4 or 5, the frequency of the alternating current signal A (t) can be determined. The multiplication factor, i.e. the number coefficient. of .1 r in equation 4 is equal to the number k of sampling pulses that do not belong to the derivation of the zeros of the alternating current signal A (t) , while the multiplication factor of If in equation 5 is equal to k + 1. Although the period Γ of the AC signal A (r) can be obtained from both Formulas 4 and 5, Formula 5 should be used when the AC current A (t) contains a transient DC component.

It 3oi now F i g. 3 considered, the detection of the phase difference between the alternating current signals A U) and B (r) will be described by simultaneously sampling at a predetermined sampling period 1 1 with the aid. According to FIG. 2, the alternating currents A (t) and ß (r) are simultaneously sampled at fj, r ₂ ... f, ₃ , f ₁₄ ... in order to obtain the corresponding instantaneous values AU ₁ ), B (I ₁ ) , A (t ₂ ), B (t ₂ ) ... A (t _n ), B (I _n ), / 4 (f ₁₄ ), B (r ₁₄ ) ... For the alternating current AU) the determination of the zeros at the times r ₂ and? _g possible, while for the alternating current signal B (t) the zeros at < ₅ and t _n can be detected. If the times.It ₁₁ , At ₁₂ , If, ',,, ItJ ₂ ,, -Ii ₁ "and Ir ₁₂ etc. can be obtained from the corresponding sampling points to the associated zero positions, the phase differences ψ between the alternating current signals A are (t) or B (t) for the times f ₅ and r ₈ :

9 = U ₁₂ + 2.If + IfJ ₁ . (6)

9 = .7 - (.lr; ₂ + 2.Ir + Jr ₁ O- (7)

So here the coefficients of .Ir in equations 6 and 7 above are equal to the number of Sampling pulses that are not relevant to the zero point extraction of the AC signal, such as the has shown the previous explanation with the aid of FIG.

As a result, the expressions for calculating the phase difference between A (t) and β (r) take both formulas 6 and 7. which depends on the zeros of the zero calculation, although the correlation between the alternating current signals A (t) and ß (r) remains invariant. This is the case because according to the invention, as can be seen from the explanation of FIG. 1 can be seen. the determination of the zeros is carried out regardless of whether the amplitude of the alternating current signal A (ί) varies from a negative to a positive value or vice versa. Therefore, it is necessary to consider the relationship between A (i) and ß (r) when either of formulas 4 and 5 are to be used.

Which of these formulas to choose can easily be determined by those shown in Figures 4a through 4k Signal curves are examined.

Fig. 4 a to 4d show signal courses in which the Phase difference 9- between the AC signals

/ I U) and ß (r) is equal to or less than y. where the Signal curves in Fig. 4a and 4b for the case V ^ 9- > Jr (Ir is the sampling period with

- ^ -> Ir> O) and the signal curves in Fig. 4c

and 4d correspond to the case U 2: 9> 0. FIGS. 4e and 4f indicate the signal profiles. in which the phase difference η is equal to zero, while FIG. 4g covers the case 9- = π. In the waveforms of

4h to 4k, y <9 < τι applies. To be more precise.

-5- <9 g (.-Τ - U) for Fig. 4h and 4i. and further

{n - Ir) < ψ g. -7 for F i g. 4j and 4k. In summary, it can be said that the waveforms in FIGS. 4a to 4d correspond to the cases where the alternating current signal A (t) is delayed in phase with respect to the alternating current signal B (t), in FIG. 4g A (t is in phase opposition to B (r), and in FIG. 4a to 4k A (t leads in phase B (r). The conditions or states a, b and c shown in FIG 4a to 4k are assigned to each signal curve diagram, give a quantitative basis for the discrimination or differentiation in the phase relation between A (t) and β (f) even if the phase relation between A (t and B (f) is like g in F i.'s 4a to 4k, the reverse traffic are the phase discrimination possible durcl merely interchanging the roles of A (t) and α B (r) ii states and b. as a result, should such au F i g. 3 It can be seen from formulas 5 and 7 that the phase difference ψ is calculated using formula 6 if one of the signal curves from FIGS. 4 to 4d is present, or using formula 7 for one of the signal curves from FIGS. 4h to 4k.

It will now be discussed how the signal waveforms of FIGS. 4a to 4k are to be interpreted. The sampling points t ₁ and t ₂ correspond to t ₄ and I ₅ , I 1 and r _a or I ₁₀ and J _n in FIG. 3. The sampling period is If. The points i ₀₁ and J ₀₂ are the points at which the alternating current signal B (f) or A {t) comes from the negative level to the positive level or from the positive level to the negative level. Namely, the alternating current signals β (f) and A (t) _{become zero at (01} and f _02, respectively. In FIGS. 4a to 4k, t _m and f _{02 are} actual or real zeros of B (t) and ~ A (t \ they can however, are regarded as the presumed or assumed zeros as obtained according to the procedure of _{FIG. 1, ie T 11} in FIG. 1. The time intervals, 1T ₁ and Ii ₀₁ become from i ₀₁ to r ₂ and from, respectively i ₀₂ to t ₂ measured.

Let us now calculate the phase difference between the alternating current signals A (t) and B (t) after the zero point of A (t) has been determined to be between f ₁ and t 2 at time t ₂ . In this case, if the following conditions are met at the same time:

a) AU ₁ ) > 0, / 4 (T ₂ ) gO,

b) BO ₁ ) ^ 0, B (t ₂ ) < 0,

c) It ₀ ,> C ₀₂ ,

the relative position of AU) and B (O is shown in the signal diagram of Fig. 4d. Formula 6 is then used to calculate the phase difference. Other signal diagrams are used for other states.

F i g. 5 is the block diagram of a basic exemplary embodiment of the invention, this exemplary embodiment being able to detect the frequency of the alternating current signal and the phase difference between different alternating current signals. The arrangement in FIG. 5 has two inputs Pur alternating current signals A (t) and B (t), but only one of the two signals A (t) and ß (f) needs to be used. A clock pulse generator 11 generates a sequence of clock pulses with a predetermined sampling period, It. Sampling memories 13 and 15 store the instantaneous values of the input signals AU) and B {t) when the clock pulses are received from the clock pulse generator 11, corresponding to the clock pulses that are received until the operation of an analog-to-digital converter, which will be described later, has ended. A control circuit 17 supplies predetermined control signals to various stages, which will be explained below, which are in a predetermined time position with respect to the clock pulses from the generator 11. A sampling circuit 19 forwards the output signals from the sampling memories 13 and 15 alternately as a function of a signal S 1 from the control circuit 17. An analog-to-digital converter 21 converts _{the output signals of the sampling memories 13 and 15 as a function of a signal S 2} from the control circuit 17, the output signals of the sampling memories 13 and 15, which are transmitted via the sampling circuit 19, being converted into corresponding digital signals . A buffer memory 23 stores the output signals of the analog-digital converter 21 in response to a signal S ₃ from the control circuit 17. A discriminator 25 reads the data relating to the alternating current signals A (t) and BU) from the buffer memory 23 in response from a signal S ₄ from the control circuit 17 and then performs predetermined arithmetic and discriminatory operations.

_{The signals S 1} , S ₂ , S ₃ and S ₄ output by the control circuit 17 are not of the same type, but different, so that the discriminator 25 can carry out the desired discrimination operations, as will be described later. The explanation of the block diagram in FIG. 5 and the signal curves in FIG. 1 through 4 will show how that

ίο zeroing, the period of the alternating current signal A (t) and the phase difference between the alternating current signals AU) and ß (f) are to be determined. Operations for determining quantities such as the period and the phase difference alone, however, do not fulfill the function of a protective relay as is currently used. It will therefore now be described how to use the data obtained from the circuit with the above structure to perform the functions of various protective relays.

1. Phase difference detection relay

The discriminator 25 is designed so that it generates an output signal only when the phase difference? 3 and F i g. 4 a to 4 k is obtained, is greater or less than a predetermined value ^ ₀ ,

2. Frequency detection relay

The discriminator 25 is designed so that it generates an output signal only when the period Γ

or y T, which according to the procedure of FIG. 2 is greater or less than a given time interval T ₀₁ or -j T ₀₁ (or T ₀₂ or y T ₀₂ ),

3. Peak value detection relay

The excitation or de-excitation of a relay, such as an overvoltage relay, an overcurrent relay or an undervoltage relay, which is activated when a peak value is detected in an alternating current signal A (t , is determined as follows:

As can be seen from the signal diagram of FIG. 2 shows, time can. If ₁₂ from the time r ₂ to the zero point of the alternating current signal AU) correspond to that in FIG. 1 after the AC signal AU) has been sampled at f. The instantaneous value or sample value AU2) of ^the alternating current signal AU) at the time point f ₂ is given by the equation:

AU ₂ ) = A _max sin (Jf ₁₂ ),

where A _{max is} the peak amplitude of the alternating current signal A (t) . Hence the peak A _{mc is given} by the expression:

A max -

\ A (I ₂ )]

I sin (.If ₁₂ ) I.

which can be expressed using only the data available _{at time f 2.} The "Ablas values A (I ₃ ) and A (U) of the alternating current signal A ( at times f ₃ and i ₄ are calculated according to d ^; formula:

AU ₃ ) = A _max sm (Jf +, If ₁₂ )
Λ (U) = Λ »« sin (2 Jf + ..H ₁₂ ).

(8 ") 309548/3

Accordingly, the peak value can be obtained using the following formulas:

A -

" max

A -

^ ¹ max

I AU ₃ )

I sin (., Ir + Ji ₁₂ ) I.

\ A (t _A ) \
I sin (2.If + .Ji ₁₂ ) I

circuit, given by Fsin ™ ι or 1 sin mi - 7, the impedance Z, the reactance X and the resistance value R of the circuit are determined by the following formulas:

For other sampling points I ₅ . t _b ... similar formulas are determined using similar investigations.

The peak value can thus be obtained for each sampling point, so that a protective device which responds to the peak value of the input or input signal can be realized by such an approach. In this case, a more reliable discrimination could be expected if it is ensured before the operation of the protective device that all the calculated results for some successive sampling points satisfy a predetermined condition, or if the peak value for fc.If + If ₁₂

in close proximity to y is used as the anomaly discrimination criterion, where k is the number of sampling pulses that have nothing to do with the derivative of the zeros of the signal.

4. Power measurement relay

The excitation or de-excitation of such a relay as a power direction relay or as a power exchange monitoring relay, which is used by detecting a quantity corresponding to the product of voltage and current is determined as follows:

Assume that the alternating current signals AU) and B (t) in Fig. 3 are the voltage Fsinmf and the current / sin (o> t -9-), respectively: in this case the phase difference 7 between the voltage and the current according to the procedure of FIG. 3 and 4 can be won. It can also be seen from the above discussion of the peak value detection relay that the peak value of the voltage or the current can be determined for each sampling point.

On the other hand, the power P as the product of voltage and current is given by the expression:

P = VI cos <f. (10)

Therefore, the power P can be obtained from separately obtained quantities V, I and φ by first forming cos φ from φ and then forming the product of V, I and cos 9. The power calculated in this way is then used as a discrimination criterion for the disturbance. In this case, a special value of cos 7 can be derived from one of the previously stored data of cos 7, which corresponds to a special value of ψ in order to simplify the calculation of cos 9.

5. Impedance detection relay

The excitation or de-excitation of such a relay as an impedance relay, as a distance relay or as a conductance relay, as a direction distance relay to serve, which detects a quantity corresponding to the ratio of voltage to current is determined as follows:

It is well known that when the voltage and the current measured in a certain alternation

V T

sin ψ, R = - sin 7. (11)

Therefore only the voltage to current ratio for the impedance relay needs to be calculated. For the reactance relay or the resistance value relay, it is also only necessary to set sin 9 or cos <f

to be determined from 7 and the product -y- sin 9 or

¹ S ycos? to calculate. In this case, with the power measurement relay, a special value of sin 9 or cos 7 is obtained from one of the data of sin 9 or cos φ which have been previously stored for different values of ψ , which corresponds to a special value of ψ.

F i g. 6 shows an impedance diagram of a conductance relay, with the resistance on the abscissa and the reactance are plotted on the ordinate.

From Fig. 6 it can be seen that the conductance relay _{corresponds to an impedance relay (with a setting impedance Z 0} ) that has been shifted parallel from the coordinate origin to a point whose abscissa and ordinate are equal to a setting resistance R ₀ and a setting reactance X ₀ , respectively. Therefore, by using Z, X and R obtained from Equations 11, the following relationship is obtained:

(X ₀ - Xf + (K ₀ - R) ² ^

(12)

In order to perform the function of a conductance relay, the discriminator 25 is designed so that it has an output signal only outputs if the condition according to equation 12 is met.

It can thus be seen that the arrangement according to the invention (according to FIG. 5) has the functions of various Types of Schulz relays can meet by the discriminator is designed appropriately. The following describes how actually the various quantities are calculated that must be obtained in order to perform the functions of the protection relays analyze.

As shown in FIG. 5 can be seen. the AC signal is sampled with a constant period, to provide the corresponding digital information.

which is then fed into the discriminator, dei on the basis of the digital information obtained, a decision is made as to whether a predetermined condition is met or not, the overall operation of the individual stages being controlled by the control circuit. the The program flowcharts given below correspond to the discrimination or decision-making operations, which are mainly used by the discriminatoi assigned.

1. Program flow chart for zero point acquisition

7 shows a program flow chart for the detection of the zeros of an alternating current signal. An operation 101 triggers a start such as an interruption. Such an interruption can be one of the sampling pulses I ₁ , t ₂ ... which have been described with reference to FIGS. 1 to 4 and which serve to trigger this program sequence for the zero point detection; it can be

also act around other signals through which the computer is adapted to other purposes.

A decision is made through a branch 103 as to whether or not the interruption is for the start of the zero position detection program flow. The program flow follows the process line YES if the interruption is provided for the start of the zero position detection process, otherwise the other process line NO. If the program flow proceeds along the flow line NO as a result of the decision made by the branch 103, the computer ends the decision operation and turns to another order or job through the operation 104. If the result of the decision through branch 103 is YES, the instantaneous value of an alternating current signal A (t) at time i ″, ie A (t ″), is read by an operation 105. An operation 107 forms the product AU _n - U ^- A (I _n ) of the instantaneous value /! (("_,) At a sampling point i" _, immediately before the sampling point t "with the value A (t") . At branch 109 it is decided whether the value of the product calculated by operation 107 is equal to or less than zero or greater than zero. If the product is equal to or less than zero, ie / 4 (i "_,) · AU _n ) <0, the program flow follows the YES flow line and arrives at an operation 111. If the product is greater than zero, ie AU "- _X ) * AU _n ) > 0. the program flow follows the NO flow line to arrive at a To go to operation 110, where the computer finishes this job and starts another job. When the result of the decision in branch 109 is YES, K ₁₁ and Ir ₁₂ are determined by operation 111 according to the method of FIG. 1 calculated. The zero point of the alternating current signal AU) can thus be calculated from the data with respect to the sampling point t ₁ or f 1. The computer then ends this job and takes up another job through an operation 113.

2. Program flow chart for the
Passage difference detection

F i g. 8 shows a program flow chart for the detection of the phase difference between the two alternating current signals A (t) and β (i). In this program flow chart, operations 101 to 111 are similar to those with the same reference numerals in the program flow of FIG. 7 designated. The only major difference is that two AC signals AU) and B (t) are input. Further, after / Jf _n and At _n are calculated by the operation 111, the operation of decreasing the coefficient k from .1 f to zero is performed, as will be described later, by an operation 112: even if so The result of the decision by the operation 109 is NO. if the computer does not immediately take up another order, instead an operation 115 is reached in order to calculate the product B (f _n _,) · B (f n). An operation 117 decides whether the product is equal to or less than zero or greater than zero. similar to that by the operation 109. If the decision result of the operation 117 is YES, that is, B (t "~ \) ■ B (t _n ) ^ 0, .It ₁ ', and Ii ₁ ', are calculated by an operation 119, to obtain the zeros of the alternating current signal B (I) . An operation 120, which will be explained in more detail later, reduces the coefficient k of It to zero. When the decision result of the operation 117 is NO, which corresponds to the point f ₃ in FIG. 3, the coefficient k is changed from If to k + 1 by adding one to it by an operation 121, where k is the factor of It which occurs in the phase difference calculation. When the decision result of operation 119 and operation 117 is YES, not only / If ₁₁ and .It _{12 become}

ίο or .IfJ ₁ and At ' _n are calculated by operation 111 or 119, but operation 133 is also reached, where the phase advance or delay between the alternating current signals AU) and BU) is detected. This detection is carried out according to the method of FIGS. 4a to 4k. An operation 125 becomes the product k ■. 1 1 the number k of sampling pulses that are not used for the extraction

■ the zero point are relevant, and the sampling period. If calculated. An operation 127 calculates the phase difference q based on the formulas 6 and 7. This phase difference calculation can end at operation 121 or 127, but for the exact simulation of the function of a relay that generates an output signal only if the relationship between the phase difference γ and a predetermined value q _{0 is} such that q ^ 9 ₀ or ψ < 9Ό, another operation 129 is provided to check this relationship. Depending on the results of the previous test, the corresponding output signals are issued or an operation 131 can be reached for another job.

3. Program flow chart for frequency acquisition

F i g. 9 shows a program flow chart for frequency detection of an AC signal AU) - In this program flow chart, operations 101 to 109 and operation 111 are the same as corresponding operations 101 to 109 and 111 in the program flow chart for zero position detection. If AU “- \) · AU _n ) > 0. the program flow follows the NO flow line to reach operation 121, where a one is added to the stored number k of sampling pulses which are not relevant to the extraction of the zero to form k + 1. The computer then accepts another job through operation 130. When the decision result of operation 109 is YES, operation 111 is reached to generate If ₁₁ and If ₁₂ . Then an operation 133 is reached to calculate a period T which is e.g. B. is calculated from Formula 5. The factor of, 1 1 at a certain particular sampling point is the value at the particular sampling point of the number fc stored in the computer at operation 121. By operation 135, the difference between the period T is obtained by operation 133, and one predetermined value T ₀ , obtained. It is then decided by an operation 137 whether or not T- T ₀₁ ^ 0. When the decision result is YES, the program flow follows the sequence line YES. to give an output signal 1 indicating that the frequency has fallen below a certain level. If the condition T - 7 " ₀₁ ^ 0 is not met, the program runs along the NO sequence logic to arrive at an operation 139. Through operation 139, T - T _{01 is} made from the period 7 'and the predetermined value 7J _{n is} calculated and performed by an operation 141

it is decided whether the calculated result satisfies the condition T - T ₀₁ ^ O. If this condition is met, the program will run along the YES flow line to provide an output 2 indicating that the frequency has risen above a certain level. On the other hand, if this condition is not met, the program will follow the NO flowline to reach operation 130. Through operation 130, the computer takes on another order or job.

4. Program flow chart door the peak value recording

10 shows a program flow chart for simulating the function of a peak value detection relay. In this case, too, the operations 101 to 109 and 111 have the same meaning as the corresponding operations in the program flow chart for zero position detection. If the decision result of operation 109 is NO, operation 129 is reached in order to store k + 1, which value has been obtained by adding a one to the number k of sampling pulses which are not relevant to the extraction of the zero. If the decision result of operation 109 is YES and therefore J t _n and J t _{12 are} calculated by operation 111, the stored number k is cleared to zero by an operation 149. An operation 151 calculates At _n + k · At , and an operation 153 calculates sin (Ji ₁₂ + k · A r). Finally, a peak value A _{max is} calculated using formulas 9, 9 'and 9 "by operation 155. Since, according to the invention, the point in time at which the sequence of calculations is started is renewed every time the AC signal becomes zero, the absolute value of a _"mx computed by an operation 157 through operation 159, the DifferenzU is." _a J -. a ₀₁ 'ert / calculated between a _max and a predetermined ^ I _01, by an operation 161 it is decided whether the state \ a _max \ - A ₀₁ ^ 0 is met or not. If this condition is met, an output signal is output 1. If this condition is not met, an operation 163 is reached in order to calculate Umaxl - Λ02, where A _{02 is} a different setting value It is then decided by an operation 165 whether or not the condition \ A _ma J - A ₀₂ ^ 0 is fulfilled If the condition is fulfilled, an output signal 2 is given, while otherwise an operation 167 is reached so that the Calculator a another job. Since the output signal 1 is obtained when \ A _m

performed even after the operations by which the voltage peak value, the current peak value and the phase difference are obtained. In the program flow chart of FIG. 11, there is first an operation for obtaining the phase difference φ, secondly an operation for obtaining peak values, and finally an operation for calculating power. Correspondingly, the operations before an operation 171, where sin At ₁₂ + k · At + φ is calculated, are equivalent to the corresponding operations in the program flow in FIG. 1, with the exception of an additional operation 124. 8. Operation 124 is described below. The peak values of voltage and current are obtained by operations 171 to 177, but the recovery of the peak values is the same as in the case where two input signals are applied to operations 153 and 157 in the flow of FIG. The reason why the calculation by operation 171 is associated with an angle (Af ₁₂ + k-.it + ψ) and each operation 175 with an angle UJtu + k-At + ψ) will be explained below. Let us now consider the case where the calculation is performed with reference to the sampling point I ₆ . With regard to B {t) , the peak value B _{max is given} by the following formula:

A ₀₁ S 0

the output signal 1 occurs for \ A _max ] - A ₀₁ . The output signal 1 is equivalent to the output signal from a relay such as an undervoltage relay. Output signal 2 is issued similarly ^when UmJ - A ₀₁ ^ 0 applies, ie \ A _m J ^ A ₀₁ , therefore output signal 2 corresponds to the output signal from a relay such as an overvoltage relay or an overcurrent relay.

5. Program flow chart for the recording of services

11 shows a program flow chart for simulating the function of the power detection relay described above. As has already been explained in connection with the explanation of a power detection relay, the peak values of the voltage and the current together with the phase difference φ between them are required in order to calculate the power. Hence the calculation of the power

55

60

IJ '* ^{o /} '

^Dma * - | sin (ir; ₂ + li) | '

while the peak value of A (t), i.e. A _max should be calculated:

"max ~

\ A (t _b ) \

I sin (IiZ ₂ + Ii + ψ) \ '

The forms of these formulas are interchanged in the calculation at sampling point t _g , that is, the phase difference q is taken into account in the calculation of B _max. Operation 124 determines which of operations 171 and 175 the phase difference ψ should be applied to. That is, for each sampling point after the zero of A (t) the phase difference is fed to operation 175, where the calculation of B _{max is} prepared, while for each sampling point after the zero of B (t) the phase difference is fed to operation 171 where the calculation of A _{max is} prepared. A (tf and β (f) respectively mean voltage and current and current and voltage, respectively. P = VI cos y is calculated by an operation 179. In this case, a special value of cos γ can be obtained from one of the cos ir values which have been previously stored, namely corresponding to a special value of φ. An operation 181 detects the difference between the power P obtained in this way and a predetermined value F ₀₁ , then a decision is made as to whether the difference is zero or negative, by an operation 183. If the difference is zero or positive, an output signal is given, otherwise an operation 185 is reached so that the computer accepts another job.

6. Program flow chart for impedance acquisition

Fig. 12 shows a program flow chart for simulating the function of that described above Impedance relay. From formula 11 it can be seen that the impedance relay can also be simulated

(O

by obtaining V, I and cos φ so that operations 101 through 177 in FIG. 12 can be completely replaced by the corresponding operations in the program flow chart of FIG. Operations 191, 193, and 195 compute Z, X, and R, respectively. An operation 197 decides whether the conductance characteristic of FIG. 6 is satisfied or not, a further decision is made by an operation 199. If the decision result is YES, an output signal is given, otherwise, 0, an operation 201 is reached and the computer takes up another job.

F i g. FIG. 13 shows an exemplary embodiment of the discriminator 25, which consists of several units, each of which has a single function, and for the phase difference detection, which is based on FIG. 8 is designed. Normally the arithmetic unit of a digital computer is used as a disc minator. For a better explanation, however, the stage is shown as an interconnection of single-function units. In FIG. 13, the same reference numerals as in FIG. 13 are used as far as possible. 5 used. An interruption factor analyzer J provides e.g. B. in dependence on the output signal of the generator 11 an output signal J ₁ , which the control circuit 17, 5 controls. Correspondingly, the control circuit 17 sends a command to a memory K that the memory K is to store digital data which are transmitted via the input circuit in FIG. 5 can be obtained. The control circuit 17 sends, after receiving a signal Kl that the storage by the memory K has ended, to a multiplier L an instruction E ₂ that the product A (Q · A (I _n ^ ₁ ) is to be formed [in the case of bit) the product B (I _n ) -B (I _n ^) I

As has already been described, it can be seen that for A (Q * A (^ ₁ ) g 0 the zero point of the alternating current signal A (t) lies between t. And f _n _, A sign discriminator M distinguishes the sign of the product A (Q -A (^ ₁ ) on the basis of the data obtained from the multiplier L. If the product is positive, an output signal M _{1 is obtained-}

and Se ^;

the alternating currentsi
associated forms ^ £
knmi ⁿ ator can be determined

count them

neighboring i.e. the analogs

winaung the zero parts

keeps watch ^ ow

»Use, will. W- fcA ^ gl S

these signal diagrams ^ (O and B (Q odeτ / U, - J and Btf.-i) are compared and the times I ₀₁ and I _{02 are} reverberated., Fig. 4

ng in phase dis with reference to Figures 4a through 4k. A counter 0 η between two be alternating current signals, "jlse, which are not used for _C11C6 -en. The counter 0 over output signal of the sign - • One to the number! "" ■ · sampling pulses stored there, if d

output signal is positive, ie M ₁ , and ^ ges, xicLte number information if the output

signal is zero or negative, i.e. M ₂ . The ^ interval r ₂ - r ₄ in F i g. 3, ie 2 A t m of formula 6, can

ΪΑίίίϊβϊβ

flow chart of Fig. 8. A phase difference calculator Q calculates the phase difference between alternating current signals AW and B (t) from the output signal of the counter 0, the output signal of the phase discriminator * JV, A (t) and B (t), A (Q and A ( l, -i and BU ,) The phase discriminator N not only shows the phase position between the alternating current signals A (t) and B (t) , but also provides the

30th

35

₄ o

the analog data into the corresponding difital data B

nen can also in the case of the alternating current signal B (t) counter U.

the end

¹ * -

In addition 5 sheets of drawings

Claims (6)

Patent claims: 1. A method for digitally determining the position of the zero crossings of a sinusoidal alternating current signal, characterized in that the alternating current signal with a fixed sampling period Ji = t " - t _n _ _lt is less than half the period T of the alternating current signal, in its amplitude A ( t) is sampled, that the determined amplitude values are stored over a predeterminable time and are multiplied in pairs for two consecutive samplings, that the sign of the amplitude value products obtained is determined and that for each amplitude value pair A (I _n ^ ₁ ) and A (t _n ), for which a product -4 (t "_i) - A {t") <0 results, the point of intersection of the abscissa for a straight line passing through these amplitude values is calculated (FIG. 1). 2. The method according to claim 1, characterized in that the frequency of the alternating current signal is determined by taking the period T of the alternating current signal from the time interval is obtained between two successive zeros of the alternating current signal (FIG. 2). 3. The method according to claim 1, characterized in that the phase difference between two different alternating current signals is determined from two successive zeros of the one of the two alternating current signals and the zero point of the other of the two alternating current signals, those in the time interval between the two successive zeros of the former AC signal falls (Fig. 3). 4. The method according to claim 3, characterized in that from two alternating current signals from which one of the alternating voltage at the ends of a consumer and the other to the Consumers flowing alternating current corresponds, the impedance of the consumer is determined dmch calculation of the quotient of voltage and current, taking into account the Phase difference. 5. The method according to claim 3, characterized in that from two alternating current signals from which one of the alternating voltage at the ends of a consumer and the other to the Consumers flowing alternating current corresponds to the power in the consumer as the product AC current, AC voltage and cosine of the obtained phase difference is calculated. 6. The method according to claim 1, characterized in that that the peak value of the alternating current signal is obtained as the quotient of a Sample of the AC signal and the sine of an angle corresponding to the time interval between the sampling time corresponding to this sampling value and the nearest zero point of the AC signal corresponds.